Machine learning for metabolites

Goal: can machine learning methods help us to associate metabolites with leaf length?

Previously (script 11b2) I filtered out unnamed metabolites. Here I keep them all.

Also I will PC separately for root and leaf.

library(glmnet)

Loading required package: Matrix
Loaded glmnet 4.0-2

library(relaimpo)

Loading required package: MASS
Loading required package: boot
Loading required package: survey
Loading required package: grid
Loading required package: survival

Attaching package: ‘survival’

The following object is masked from ‘package:boot’:

    aml


Attaching package: ‘survey’

The following object is masked from ‘package:graphics’:

    dotchart

Loading required package: mitools
This is the global version of package relaimpo.

If you are a non-US user, a version with the interesting additional metric pmvd is available

from Ulrike Groempings web site at prof.beuth-hochschule.de/groemping.

library(tidyverse)

Registered S3 methods overwritten by 'dbplyr':
  method         from
  print.tbl_lazy     
  print.tbl_sql      
── Attaching packages ───────────────────────────────────────────────────────────────────────────────────────────── tidyverse 1.3.0 ──
✓ ggplot2 3.3.3     ✓ purrr   0.3.4
✓ tibble  3.0.4     ✓ dplyr   1.0.2
✓ tidyr   1.1.2     ✓ stringr 1.4.0
✓ readr   1.4.0     ✓ forcats 0.5.0
── Conflicts ──────────────────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
x tidyr::expand() masks Matrix::expand()
x dplyr::filter() masks stats::filter()
x dplyr::lag()    masks stats::lag()
x tidyr::pack()   masks Matrix::pack()
x dplyr::select() masks MASS::select()
x tidyr::unpack() masks Matrix::unpack()

get leaflength data

leaflength <- read_csv("../../plant/output/leaf_lengths_metabolite.csv") %>%
  mutate(pot=str_pad(pot, width=3, pad="0"),
         sampleID=str_c("wyo", genotype, pot, sep="_")) %>%
  select(sampleID, leaf_avg_std) 

── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  pot = col_double(),
  soil = col_character(),
  genotype = col_character(),
  trt = col_character(),
  leaf_avg = col_double(),
  leaf_avg_std = col_double()
)

leaflength %>% arrange(sampleID)

get and wrangle metabolite data

met_raw <-read_csv("../input/metabolites_set1.csv")

── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────────────
cols(
  .default = col_double(),
  tissue = col_character(),
  soil = col_character(),
  genotype = col_character(),
  autoclave = col_character(),
  time_point = col_character(),
  concatenate = col_character()
)
ℹ Use `spec()` for the full column specifications.

met <- met_raw %>% 
  mutate(pot=str_pad(pot, width = 3, pad = "0")) %>%
  mutate(sampleID=str_c("wyo", genotype, pot, sep="_")) %>%
  select(sampleID, genotype, tissue, sample_mass = `sample_mass mg`, !submission_number:concatenate) %>%
  pivot_longer(!sampleID:sample_mass, names_to = "metabolite", values_to = "met_amount") %>%
  
  #adjust by sample mass
  mutate(met_per_mg=met_amount/sample_mass) %>%
  
  #scale and center
  group_by(metabolite, genotype, tissue) %>%
  mutate(met_per_mg=scale(met_per_mg),
         met_amt=scale(met_amount)
  ) %>% 
  pivot_wider(id_cols = sampleID, 
              names_from = c(tissue, metabolite), 
              values_from = starts_with("met_"),
              names_sep = "_")

met 

split this into two data frames, one normalized by tissue amount and one not.

met_per_mg <- met %>% select(sampleID,  starts_with("met_per_mg")) %>%
  as.data.frame() %>% column_to_rownames("sampleID")
met_amt <- met %>% select(sampleID,  starts_with("met_amt")) %>%
  as.data.frame() %>% column_to_rownames("sampleID")

get leaf data order to match

leaflength <- leaflength[match(met$sampleID, leaflength$sampleID),]
leaflength

Calc PCAs:

normalized

leaf

met_per_mg.leaf_PCA <- met_per_mg %>% 
  select(matches("_leaf_")) %>%
  prcomp(center = FALSE, scale. = FALSE) #already centered and scaled
names(met_per_mg.leaf_PCA)

[1] "sdev"     "rotation" "center"   "scale"    "x"       

tibble(variance=met_per_mg.leaf_PCA$sdev^2, PC=str_c("PC", 
                                                      str_pad(1:length(met_per_mg.leaf_PCA$sdev), width = 2, pad="0"))) %>%
  mutate(percent_var=100*variance/sum(variance),  
         cumulative_var=cumsum(percent_var)) %>%
  magrittr::extract(1:15,) %>%
  ggplot(aes(x=PC, y=percent_var)) +
  geom_col(fill="skyblue") + 
  geom_line(aes(y=cumulative_var), group="") +
  ggtitle("percent variance explained, named, normalized leaf metabolites")

root

met_per_mg.root_PCA <- met_per_mg %>% 
  select(matches("_root_")) %>%
  prcomp(center = FALSE, scale. = FALSE) #already centered and scaled
names(met_per_mg.root_PCA)

[1] "sdev"     "rotation" "center"   "scale"    "x"       

tibble(variance=met_per_mg.root_PCA$sdev^2, PC=str_c("PC", 
                                                      str_pad(1:length(met_per_mg.root_PCA$sdev), width = 2, pad="0"))) %>%
  mutate(percent_var=100*variance/sum(variance),  
         cumulative_var=cumsum(percent_var)) %>%
  magrittr::extract(1:15,) %>%
  ggplot(aes(x=PC, y=percent_var)) +
  geom_col(fill="skyblue") + 
  geom_line(aes(y=cumulative_var), group="") +
  ggtitle("percent variance explained, named, normalized root metabolites")

raw

leaf

met_amt.leaf_PCA <- met_amt %>%
  select(matches("_leaf_")) %>%
  prcomp(center = FALSE, scale. = FALSE) #already centered and scaled
names(met_per_mg.leaf_PCA)

[1] "sdev"     "rotation" "center"   "scale"    "x"       

tibble(variance=met_amt.leaf_PCA$sdev^2, PC=str_c("PC", 
                                                   str_pad(1:length(met_amt.leaf_PCA$sdev), width = 2, pad="0"))) %>%
  mutate(percent_var=100*variance/sum(variance),  
         cumulative_var=cumsum(percent_var)) %>%
  magrittr::extract(1:15,) %>%
  ggplot(aes(x=PC, y=percent_var)) +
  geom_col(fill="skyblue") + 
  geom_line(aes(y=cumulative_var), group="") +
  ggtitle("percent variance explained, named, raw leaf metabolites")

root

met_amt.root_PCA <- met_amt %>%
  select(matches("_root_")) %>%
  prcomp(center = FALSE, scale. = FALSE) #already centered and scaled
names(met_per_mg.root_PCA)

[1] "sdev"     "rotation" "center"   "scale"    "x"       

tibble(variance=met_amt.root_PCA$sdev^2, PC=str_c("PC", 
                                                   str_pad(1:length(met_amt.root_PCA$sdev), width = 2, pad="0"))) %>%
  mutate(percent_var=100*variance/sum(variance),  
         cumulative_var=cumsum(percent_var)) %>%
  magrittr::extract(1:15,) %>%
  ggplot(aes(x=PC, y=percent_var)) +
  geom_col(fill="skyblue") + 
  geom_line(aes(y=cumulative_var), group="") +
  ggtitle("percent variance explained, named, raw root metabolites")

now try these in a penalized regression

normalized

are the PCs normalized?

colMeans(met_amt.leaf_PCA$x) %>% round(3) #yes centered

 PC1  PC2  PC3  PC4  PC5  PC6  PC7  PC8  PC9 PC10 PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23 PC24 PC25 PC26 
   0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0    0 
PC27 PC28 PC29 PC30 PC31 PC32 PC33 PC34 PC35 PC36 
   0    0    0    0    0    0    0    0    0    0 

apply(met_amt.leaf_PCA$x, 2, sd) %>% round(2) #not scaled

  PC1   PC2   PC3   PC4   PC5   PC6   PC7   PC8   PC9  PC10  PC11  PC12  PC13  PC14  PC15  PC16  PC17  PC18  PC19  PC20  PC21  PC22 
11.94  8.37  6.74  5.84  5.46  5.32  5.02  4.55  4.38  4.11  3.87  3.80  3.73  3.56  3.44  3.32  3.27  3.17  3.16  3.08  2.94  2.90 
 PC23  PC24  PC25  PC26  PC27  PC28  PC29  PC30  PC31  PC32  PC33  PC34  PC35  PC36 
 2.86  2.78  2.73  2.61  2.56  2.53  2.40  2.39  2.33  2.26  2.22  2.14  0.00  0.00 

combine the leaf and root, and then scale them:

met_per_mg.leaf_PCs <- met_per_mg.leaf_PCA$x
colnames(met_per_mg.leaf_PCs) <- str_c("leaf_", colnames(met_per_mg.leaf_PCs))

met_per_mg.root_PCs <- met_per_mg.root_PCA$x
colnames(met_per_mg.root_PCs) <- str_c("root_", colnames(met_per_mg.root_PCs))

met_per_mg.PCs <- cbind(met_per_mg.leaf_PCs, met_per_mg.root_PCs) %>%
  scale()

met_amt.leaf_PCs <- met_amt.leaf_PCA$x
colnames(met_amt.leaf_PCs) <- str_c("leaf_", colnames(met_amt.leaf_PCs))

met_amt.root_PCs <- met_amt.root_PCA$x
colnames(met_amt.root_PCs) <- str_c("root_", colnames(met_amt.root_PCs))

met_amt.PCs <- cbind(met_amt.leaf_PCs, met_amt.root_PCs) %>%
  scale()

also combine the rotations

met_per_mg.leaf_rotation <- met_per_mg.leaf_PCA$rotation %>%
  as.data.frame() %>% 
  rename_with(~ str_c("leaf_", .x)) %>%
  rownames_to_column("metabolite")

met_per_mg.root_rotation <- met_per_mg.root_PCA$rotation %>%
  as.data.frame() %>% 
  rename_with(~ str_c("root_", .x)) %>%
  rownames_to_column("metabolite")

met_per_mg.PC_rotation <- full_join(met_per_mg.leaf_rotation, met_per_mg.root_rotation, by="metabolite")

met_amt.leaf_rotation <- met_amt.leaf_PCA$rotation %>% 
  as.data.frame() %>% 
  rename_with(~ str_c("leaf_", .x)) %>%
  rownames_to_column("metabolite")

met_amt.root_rotation <- met_amt.root_PCA$rotation %>%
  as.data.frame() %>% 
  rename_with(~ str_c("root_", .x)) %>%
  rownames_to_column("metabolite")

met_amt.PC_rotation <- full_join(met_amt.leaf_rotation, met_amt.root_rotation, by="metabolite")

met_per_mg_fit1LOO <- cv.glmnet(x=met_per_mg.PCs, y=leaflength$leaf_avg_std, nfolds = nrow(met_per_mg.PCs), alpha=1 )

Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per fold

plot(met_per_mg_fit1LOO)

bestlam=met_per_mg_fit1LOO$lambda.1se

NEXT STEP: Do a K-fold CV, repeat many times and average. Might as well do alpha while we are at it. If we are doing alpha, then we need to manually create our own folds list for each run

normalized

multi CV

Fit 101 CVs for each of 11 alphas

set.seed(1245)

folds <- tibble(run=1:101) %>% 
  mutate(folds=map(run, ~ sample(rep(1:6,6))))

system.time (met_per_mg_multiCV <- expand_grid(run=1:100, alpha=round(seq(0,1,.1),1)) %>%
               left_join(folds, by="run") %>%
               mutate(fit=map2(folds, alpha, ~ cv.glmnet(x=met_per_mg.PCs, y=leaflength$leaf_avg_std, foldid = .x, alpha=.y
                                                         )))
             #, lambda=exp(seq(-5,0,length.out = 50)) )))
) #100 seconds

   user  system elapsed 
 93.102   4.877 118.425 

head(met_per_mg_multiCV)

for each fit, pull out the mean cv error, lambda, min lambda, and 1se lambda

met_per_mg_multiCV <- met_per_mg_multiCV %>%
  mutate(cvm=map(fit, magrittr::extract("cvm")),
         lambda=map(fit, magrittr::extract("lambda")),
         lambda.min=map_dbl(fit, magrittr::extract("lambda.min" )),
         lambda.1se=map_dbl(fit, magrittr::extract("lambda.1se")),
         nzero=map(fit, magrittr::extract("nzero"))
  )

head(met_per_mg_multiCV)

now calculate the mean and sem of cvm and min,1se labmdas. These need to be done separately because of the way the grouping works

met_per_mg_summary_cvm <- met_per_mg_multiCV %>% dplyr::select(-fit, -folds) %>% 
  unnest(c(cvm, lambda)) %>%
  group_by(alpha, lambda) %>%
  summarize(meancvm=mean(cvm), sem=sd(cvm)/sqrt(n()), high=meancvm+sem, low=meancvm-sem)

`summarise()` regrouping output by 'alpha' (override with `.groups` argument)

met_per_mg_summary_cvm

met_per_mg_summary_lambda <- met_per_mg_multiCV %>% dplyr::select(-fit, -folds, -cvm) %>% 
  group_by(alpha) %>%
  summarize(
    lambda.min.sd=sd(lambda.min), 
    lambda.min.mean=mean(lambda.min),
    #lambda.min.med=median(lambda.min), 
    lambda.min.high=lambda.min.mean+lambda.min.sd,
    #lambda.min.low=lambda.min.mean-lambda.min.sem,
    #lambda.1se.sem=sd(lambda.1se)/sqrt(n()), 
    lambda.1se.mean=mean(lambda.1se),
    #lambda.1se.med=median(lambda.1se), 
    #lambda.1se.high=lambda.1se+lambda.1se.sem,
    #lambda.1se.low=lambda.1se-lambda.1se.sem,
    nzero=nzero[1],
    lambda=lambda[1]
  )

`summarise()` ungrouping output (override with `.groups` argument)

met_per_mg_summary_lambda

plot it

met_per_mg_summary_cvm %>%
  #filter(alpha!=0) %>% # worse than everything else and throwing the plots off
  ggplot(aes(x=log(lambda), y= meancvm,  ymin=low, ymax=high)) +
  geom_ribbon(alpha=.25) +
  geom_line(aes(color=as.character(alpha))) +
  facet_wrap(~ as.character(alpha)) +
   coord_cartesian(xlim=(c(-5,0))) +
  geom_vline(aes(xintercept=log(lambda.min.mean)), alpha=.5, data=met_per_mg_summary_lambda) +
  geom_vline(aes(xintercept=log(lambda.min.high)), alpha=.5, data=met_per_mg_summary_lambda, color="blue") 

So overall these look more reasonable than the LOO plot.

Make a plot of MSE at minimum lambda for each alpha

met_per_mg_summary_cvm %>% 
  group_by(alpha) %>%
  filter(rank(meancvm, ties.method = "first")==1) %>%
  ggplot(aes(x=alpha,y=meancvm,ymin=low,ymax=high)) +
  geom_ribbon(color=NA, fill="gray80") +
  geom_line() +
  geom_point()

not a particular large difference there, aside from 0.1 and even then, not too much better.

Plot the number of nzero coefficients

met_per_mg_summary_lambda %>%
  unnest(c(lambda, nzero)) %>%
  group_by(alpha) %>%
  filter(abs(lambda.min.mean-lambda)==min(abs(lambda.min.mean-lambda))  ) %>%
  ungroup() %>%

ggplot(aes(x=as.character(alpha), y=nzero)) +
  geom_point() +
  ggtitle("Number of non-zero coefficents at minimum lambda") +
  ylim(0,36)

OK let’s do repeated test train starting from these CV lambdas

multi_tt <- function(lambda, alpha, n=10000, sample_size=36, train_size=30, x, y=leaflength$leaf_avg_std) {
  print(lambda)
  print(alpha)
tt <-
  tibble(run=1:n) %>%
  mutate(train=map(run, ~ sample(1:sample_size, train_size))) %>%
  mutate(fit=map(train, ~ glmnet(x=x[.,], y=y[.], lambda = lambda, alpha = alpha ))) %>%
  
  mutate(pred=map2(fit, train, ~ predict(.x, newx = x[-.y,]))) %>%
  mutate(cor=map2_dbl(pred, train, ~ cor(.x, y[-.y])  )) %>%
  mutate(MSE=map2_dbl(pred, train, ~ mean((y[-.y] - .x)^2))) %>%
  summarize(
    num_na=sum(is.na(cor)), 
    num_lt_0=sum(cor<=0, na.rm=TRUE),
    avg_cor=mean(cor, na.rm=TRUE),
    avg_MSE=mean(MSE))
tt
}

per_mg_fit_test_train <- met_per_mg_summary_lambda %>% 
  select(alpha, lambda.min.mean)

per_mg_fit_test_train <- met_per_mg_multiCV %>%
  filter(run==1) %>%
  select(alpha, fit) %>%
  right_join(per_mg_fit_test_train)

Joining, by = "alpha"

per_mg_fit_test_train <- per_mg_fit_test_train %>%
  mutate(pred_full=map2(fit, lambda.min.mean, ~ predict(.x, s=.y, newx=met_per_mg.PCs)),
         full_R=map_dbl(pred_full, ~ cor(.x, leaflength$leaf_avg_std)),
         full_MSE=map_dbl(pred_full, ~ mean((leaflength$leaf_avg_std-.x)^2))) %>%
  
  mutate(tt=map2(lambda.min.mean, alpha, ~ multi_tt(lambda=.x, alpha=.y, x=met_per_mg.PCs)))

[1] 13.36988
[1] 0
[1] 0.7666849
[1] 0.1
[1] 0.8732274
[1] 0.2
[1] 0.6950232
[1] 0.3
[1] 0.6122284
[1] 0.4
[1] 0.5404081
[1] 0.5
[1] 0.4719584
[1] 0.6
[1] 0.4194147
[1] 0.7
[1] 0.3761253
[1] 0.8
[1] 0.3410749
[1] 0.9
[1] 0.3097519
[1] 1

(per_mg_fit_test_train <- per_mg_fit_test_train %>% unnest(tt))

per_mg_fit_test_train %>%
  ggplot(aes(x=alpha)) +
  geom_line(aes(y=avg_cor), color="red") +
  geom_point(aes(y=avg_cor), color="red") +
  geom_line(aes(y=avg_MSE), color="blue") +
  geom_point(aes(y=avg_MSE), color="blue")

alpha of 0.8 to 1.0 are very similar and are the best here.

look at fit:

alpha_per_mg <- .8

best_per_mg <- per_mg_fit_test_train %>% filter(alpha == alpha_per_mg) 
best_per_mg_fit <- best_per_mg$fit[[1]]
best_per_mg_lambda <- best_per_mg$lambda.min.mean

per_mg_coef.tb <- coef(best_per_mg_fit, s=best_per_mg_lambda) %>% 
  as.matrix() %>% as.data.frame() %>% 
  rownames_to_column(var="PC") %>%
  rename(beta=`1`)
  
per_mg_coef.tb %>% filter(beta!=0) %>% arrange(beta)

NA

pred and obs

plot(leaflength$leaf_avg_std, best_per_mg$pred_full[[1]])

cor.test(leaflength$leaf_avg_std, best_per_mg$pred_full[[1]]) #.57

    Pearson's product-moment correlation

data:  leaflength$leaf_avg_std and best_per_mg$pred_full[[1]]
t = 4.1276, df = 34, p-value = 0.0002243
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.3076242 0.7617163
sample estimates:
      cor 
0.5777675 

best_per_mg$full_MSE

[1] 0.7717674

Percent variance explained

per_mg_vars <- per_mg_coef.tb %>% 
  filter(beta !=0, PC!="(Intercept)") %>%
  pull(PC) %>% c("leaf_avg_std", .)

per_mg_relimp <- leaflength %>% select(leaf_avg_std) %>% cbind(met_per_mg.PCs) %>% as.data.frame() %>% dplyr::select(all_of(per_mg_vars)) %>%
  calc.relimp() 

per_mg_coef.tb <- per_mg_relimp@lmg %>% as.matrix() %>% as.data.frame() %>%
  rownames_to_column("PC") %>%
  rename(PropVar_met_per_mg=V1) %>%
  full_join(per_mg_coef.tb) %>%
  arrange(desc(PropVar_met_per_mg))

Joining, by = "PC"

per_mg_coef.tb

NA

Checkout the rotations.

met_per_mg_rotation_out <- met_per_mg.PC_rotation %>% 
  pivot_longer(-metabolite, names_to="PC", values_to="loading") %>%
  filter(PC %in% filter(per_mg_coef.tb, beta!=0)$PC ) %>%
  group_by(PC) %>%
    filter(!str_detect(metabolite,".*(leaf|root)_[0-9]*$")) %>%
  filter(abs(loading) >= 0.05) %>%
  left_join(per_mg_coef.tb, by="PC") %>%
  arrange(desc(abs(beta)), desc(abs(loading))) %>%
  mutate(organ=ifelse(str_detect(metabolite, "_leaf_"), "leaf", "root"),
         transformation="normalized",
         metabolite=str_remove(metabolite, "met_per_mg_(root|leaf)_"),
         metabolite_effect_on_leaf=ifelse(beta*loading>0, "increase", "decrease"))
met_per_mg_rotation_out %>%  write_csv("../output/Leaf_associated_metabolites_normalized.csv")

met_per_mg_rotation_out

non-normazlized

multi CV

Fit 101 CVs for each of 11 alphas

set.seed(1245)

folds <- tibble(run=1:101) %>% 
  mutate(folds=map(run, ~ sample(rep(1:6,6))))

system.time (met_amt_multiCV <- expand_grid(run=1:100, alpha=round(seq(0,1,.1),1)) %>%
               left_join(folds, by="run") %>%
               mutate(fit=map2(folds, alpha, ~ cv.glmnet(x=met_amt.PCs, y=leaflength$leaf_avg_std, foldid = .x, alpha=.y
                                                         )))
             #, lambda=exp(seq(-5,0,length.out = 50)) )))
) #100 seconds

   user  system elapsed 
 70.687   2.897  87.024 

head(met_amt_multiCV)

for each fit, pull out the mean cv error, lambda, min lambda, and 1se lambda

met_amt_multiCV <- met_amt_multiCV %>%
  mutate(cvm=map(fit, magrittr::extract("cvm")),
         lambda=map(fit, magrittr::extract("lambda")),
         lambda.min=map_dbl(fit, magrittr::extract("lambda.min" )),
         lambda.1se=map_dbl(fit, magrittr::extract("lambda.1se")),
         nzero=map(fit, magrittr::extract("nzero"))
  )

head(met_amt_multiCV)

now calculate the mean and sem of cvm and min,1se labmdas. These need to be done separately because of the way the grouping works

met_amt_summary_cvm <- met_amt_multiCV %>% dplyr::select(-fit, -folds) %>% 
  unnest(c(cvm, lambda)) %>%
  group_by(alpha, lambda) %>%
  summarize(meancvm=mean(cvm), sem=sd(cvm)/sqrt(n()), high=meancvm+sem, low=meancvm-sem)

`summarise()` regrouping output by 'alpha' (override with `.groups` argument)

met_amt_summary_cvm

met_amt_summary_lambda <- met_amt_multiCV %>% dplyr::select(-fit, -folds, -cvm) %>% 
  group_by(alpha) %>%
  summarize(
    lambda.min.sd=sd(lambda.min), 
    lambda.min.mean=mean(lambda.min),
    #lambda.min.med=median(lambda.min), 
    lambda.min.high=lambda.min.mean+lambda.min.sd,
    #lambda.min.low=lambda.min.mean-lambda.min.sem,
    #lambda.1se.sem=sd(lambda.1se)/sqrt(n()), 
    lambda.1se.mean=mean(lambda.1se),
    #lambda.1se.med=median(lambda.1se), 
    #lambda.1se.high=lambda.1se+lambda.1se.sem,
    #lambda.1se.low=lambda.1se-lambda.1se.sem,
    nzero=nzero[1],
    lambda=lambda[1]
  )

`summarise()` ungrouping output (override with `.groups` argument)

met_amt_summary_lambda

plot it

met_amt_summary_cvm %>%
  #filter(alpha!=0) %>% # worse than everything else and throwing the plots off
  ggplot(aes(x=log(lambda), y= meancvm,  ymin=low, ymax=high)) +
  geom_ribbon(alpha=.25) +
  geom_line(aes(color=as.character(alpha))) +
  facet_wrap(~ as.character(alpha)) +
   coord_cartesian(xlim=(c(-5,0))) +
  geom_vline(aes(xintercept=log(lambda.min.mean)), alpha=.5, data=met_amt_summary_lambda) +
  geom_vline(aes(xintercept=log(lambda.min.high)), alpha=.5, data=met_amt_summary_lambda, color="blue") 

Make a plot of MSE at minimum lambda for each alpha

met_amt_summary_cvm %>% 
  group_by(alpha) %>%
  filter(rank(meancvm, ties.method = "first")==1) %>%
  ggplot(aes(x=alpha,y=meancvm,ymin=low,ymax=high)) +
  geom_ribbon(color=NA, fill="gray80") +
  geom_line() +
  geom_point()

not a particular large difference here after 0.2

Plot the number of nzero coefficients

met_amt_summary_lambda %>%
  unnest(c(lambda, nzero)) %>%
  group_by(alpha) %>%
  filter(abs(lambda.min.mean-lambda)==min(abs(lambda.min.mean-lambda))  ) %>%
  ungroup() %>%

ggplot(aes(x=as.character(alpha), y=nzero)) +
  geom_point() +
  ggtitle("Number of non-zero coefficents at minimum lambda") +
  ylim(0,36)

OK let’s do repeated test train starting from these CV lambdas

multi_tt <- function(lambda, alpha, n=10000, sample_size=36, train_size=30, x, y=leaflength$leaf_avg_std) {
  print(lambda)
  print(alpha)
tt <-
  tibble(run=1:n) %>%
  mutate(train=map(run, ~ sample(1:sample_size, train_size))) %>%
  mutate(fit=map(train, ~ glmnet(x=x[.,], y=y[.], lambda = lambda, alpha = alpha ))) %>%
  
  mutate(pred=map2(fit, train, ~ predict(.x, newx = x[-.y,]))) %>%
  mutate(cor=map2_dbl(pred, train, ~ cor(.x, y[-.y])  )) %>%
  mutate(MSE=map2_dbl(pred, train, ~ mean((y[-.y] - .x)^2))) %>%
  summarize(
    num_na=sum(is.na(cor)), 
    num_lt_0=sum(cor<=0, na.rm=TRUE),
    avg_cor=mean(cor, na.rm=TRUE),
    avg_MSE=mean(MSE))
tt
}

amt_fit_test_train <- met_amt_summary_lambda %>% 
  select(alpha, lambda.min.mean)

amt_fit_test_train <- met_amt_multiCV %>%
  filter(run==1) %>%
  select(alpha, fit) %>%
  right_join(amt_fit_test_train)

Joining, by = "alpha"

amt_fit_test_train <- amt_fit_test_train %>%
  mutate(pred_full=map2(fit, lambda.min.mean, ~ predict(.x, s=.y, newx=met_amt.PCs)),
         full_R=map_dbl(pred_full, ~ cor(.x, leaflength$leaf_avg_std)),
         full_MSE=map_dbl(pred_full, ~ mean((leaflength$leaf_avg_std-.x)^2))) %>%
  
  mutate(tt=map2(lambda.min.mean, alpha, ~ multi_tt(lambda=.x, alpha=.y, x=met_amt.PCs)))

[1] 121.4399
[1] 0
[1] 0.9724185
[1] 0.1
[1] 0.6990522
[1] 0.2
[1] 0.586571
[1] 0.3
[1] 0.5167138
[1] 0.4
[1] 0.444683
[1] 0.5
[1] 0.3928743
[1] 0.6
[1] 0.3464051
[1] 0.7
[1] 0.3173148
[1] 0.8
[1] 0.2852059
[1] 0.9
[1] 0.2623291
[1] 1

(amt_fit_test_train <- amt_fit_test_train %>% unnest(tt))

amt_fit_test_train %>%
  ggplot(aes(x=alpha)) +
  geom_line(aes(y=avg_cor), color="red") +
  geom_point(aes(y=avg_cor), color="red") +
  geom_line(aes(y=avg_MSE), color="blue") +
  geom_point(aes(y=avg_MSE), color="blue")

alpha of 0.8 to 1.0 are very similar and are the best here.

look at fit:

alpha_amt <- .8

best_amt <- amt_fit_test_train %>% filter(alpha == alpha_amt) 
best_amt_fit <- best_amt$fit[[1]]
best_amt_lambda <- best_amt$lambda.min.mean

amt_coef.tb <- coef(best_amt_fit, s=best_amt_lambda) %>% 
  as.matrix() %>% as.data.frame() %>% 
  rownames_to_column(var="PC") %>%
  rename(beta=`1`)
  
amt_coef.tb %>% filter(beta!=0) %>% arrange(beta)

NA

pred and obs

plot(leaflength$leaf_avg_std, best_amt$pred_full[[1]])

cor.test(leaflength$leaf_avg_std, best_amt$pred_full[[1]]) #.736

    Pearson's product-moment correlation

data:  leaflength$leaf_avg_std and best_amt$pred_full[[1]]
t = 6.3375, df = 34, p-value = 3.15e-07
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.5372665 0.8571965
sample estimates:
      cor 
0.7359065 

best_amt$full_MSE

[1] 0.6064862

Percent variance explained

amt_vars <- amt_coef.tb %>% 
  filter(beta !=0, PC!="(Intercept)") %>%
  pull(PC) %>% c("leaf_avg_std", .)

amt_relimp <- leaflength %>% select(leaf_avg_std) %>% cbind(met_amt.PCs) %>% as.data.frame() %>% dplyr::select(all_of(amt_vars)) %>%
  calc.relimp() 

amt_coef.tb <- amt_relimp@lmg %>% as.matrix() %>% as.data.frame() %>%
  rownames_to_column("PC") %>%
  rename(PropVar_met_amt=V1) %>%
  full_join(amt_coef.tb) %>%
  arrange(desc(PropVar_met_amt))

Joining, by = "PC"

amt_coef.tb

NA

Checkout the rotations.

met_amt_rotation_out <- met_amt.PC_rotation %>% 
  pivot_longer(-metabolite, names_to="PC", values_to="loading") %>%
  filter(PC %in% filter(amt_coef.tb, beta!=0)$PC ) %>%
  group_by(PC) %>%
    filter(!str_detect(metabolite,".*(leaf|root)_[0-9]*$")) %>%
  filter(abs(loading) >= 0.05) %>%
  left_join(amt_coef.tb, by="PC") %>%
  arrange(desc(abs(beta)), desc(abs(loading))) %>%
  mutate(organ=ifelse(str_detect(metabolite, "_leaf_"), "leaf", "root"),
         transformation="raw",
         metabolite=str_remove(metabolite, "met_amt_(root|leaf)_"),
         metabolite_effect_on_leaf=ifelse(beta*loading>0, "increase", "decrease"))
met_amt_rotation_out %>%  write_csv("../output/Leaf_associated_metabolites_raw.csv")

met_amt_rotation_out